Analysis and optimization of a class of hierarchic finite element methods
Nowadays, hierarchic higher-order finite element methods (hp-FEM) become increasingly popular in computational engineering and science because of their excellent approximation properties and capability of reducing the size of finite element models dramatically. In this work, we focus on symmetric linear elliptic operators and time harmonic Maxwell's equations. It is well known that the design of suitable higher-order shape functions is essential for the performance of the hp-FEM. The question of the optimal design of shape functions is extremely difficult (already the formulation of optimality criteria is not trivial at all), and very few results stating any kind of optimality are available. The conditioning of the master element stiffness matrix is a good indicator of quality of the shape functions, and we will adopt the same approach in our case as well.
Vyvialova, Svatava, "Analysis and optimization of a class of hierarchic finite element methods" (2006). ETD Collection for University of Texas, El Paso. AAI1434291.